Boundedness of optimal matrices in extremal multigraph and digraph problems |
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Authors: | Alexander Sidorenko |
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Affiliation: | (1) Courant Institute of Math. Sci., 251 Mercer Street, 10012, N.Y., USA |
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Abstract: | We consider multigraphs in which any two vertices are joined by at mostq edges, and study the Turán-type problem for a given family of forbidden multigraphs. In the caseq=2, answering a question of Brown, Erds and Simonovits, we obtain an explicit upper bound on the size of the matrix generating an asymptotical solution of the problem. In the caseq>2 we show that some analogous statements do not hold, and so disprove a conjecture of Brown, Erds and Simonovits. |
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Keywords: | 05 C 35 05 C 50 |
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